New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation  

作　　者：袁洪春 李恒梅 许雪芬 

机构地区：[1]College of Optoelectronic Engineering,Changzhou Institute of Technology [2]School of Science,Changzhou Institute of Technology [3]School of Mathematics and Physics,Jiangsu Teachers University of Technology

出　　处：《Chinese Physics B》2013年第6期162-165,共4页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 11174114);the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 12KJD140001);the Research Foundation of Changzhou Institute of Technology of China (Grant No. YN1106)

摘　　要：By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial （TVHP）. By them and the technique of integration within an ordered product （IWOP） of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial （TVHP）. By them and the technique of integration within an ordered product （IWOP） of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.

关 键 词：two-variable Hermite polynomial entangled state representation operator identities 

分 类 号：O413.1[理学—理论物理] O174.14[理学—物理]